Federal lawmakers from New Jersey are trying to restore the full deduction for state and local taxes.

Rep. Bill Pascrell told CNBC on Thursday he and fellow Democrat Sen. Bob Menendez introduced a bill in both the House and Senate earlier this week that would repeal the $10,000 federal cap on state and local tax, or SALT, deductions. The legislation is called the "Stop Attacking Local Taxpayers (SALT) Act."

He called the cap, which is part of the GOP-backed Tax Cuts and Jobs Act passed in late 2017, an "enormous, terrible scam."

"We can't accept this," said Pascrell, a member of the House Ways and Means Committee.

"We've got to take this off the books and give people back money that they have coming to them," he said on "The Exchange."

"The Senate Finance Committee won't be revisiting the SALT deduction reforms made in the Tax Cuts and Jobs Act under Chairman Grassley's leadership," Grassley spokesman Michael Zona said. Those comments came a day after President Donald Trump said he would be "open to talking about" revising the deduction limit.

While Democrats have slammed the tax law changes, the cap even faced opposition from Republicans from the high-cost states of New Jersey, New York and California.

Pascrell, who represents the 9th District in northern New Jersey, said his constituents have been hit hard this tax season. "They're not getting back anywhere near what they thought they would be getting back."

The average household in his district is paying close to $18,000 a year in property taxes, he said.

His constituents aren't alone. According to a recent survey by the New Jersey Society of CPAs, more than 63 percent of 300 CPAs in the state said their individual and family clients earning less than $200,000 will see their federal tax bill rise thanks to the SALT cap.

To fund the return of the full SALT deduction, Pascrell and Menendez's bill would raise the amount the wealthiest Americans have to pay. The legislators want to restore the top tax rate to 39.6 percent, where it was before the new tax law brought it down to 37 percent.

"You have to have some way to offset the cost," Pascrell said. Plus, the money saved because of the new cap "was like $630 billion over 10 years" and the government was giving "corporations and those at the top of the realm more money, which is totally ridiculous."